This is a markdown cell
Here is a math expression \[ x+1 = 0 \]
Here is a more complex
\[ x^2_0 + y_1 = 0 \]
Here is how you exert greater control over the sub and superscripts
\[ x^{2y_1-2}_{opt} \]
Here is how we do a sum
\[ \sum_{i=1}^{100} x_i \]
Here is how to write an integral:
\[ \int_{0}^{\infty} dx \exp(-x^2) \]
\[ \int_{0}^{\infty} dx e^{-x^2} \]
\[ f(x,y) = \frac{\sin(xy) }{1 + \exp(x+y) } \]
\[ f(x,y) = x + y^2 \]
\[ \frac{\partial f}{\partial x} = 1 \]
\[ \frac{\partial f}{\partial y} = 2y \]
\[ \nabla f \]
\[ \nabla f = \begin{bmatrix} \frac{\partial f}{\partial x} & \frac{\partial f}{\partial y} \end{bmatrix} ^T \]
\[ \nabla f = \begin{bmatrix} \frac{\partial f}{\partial x} \\ \frac{\partial f}{\partial y} \end{bmatrix} \]
The Identity in 3D
\[ I = \begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{bmatrix} \]